5x^2+11x=8

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Solution for 5x^2+11x=8 equation:


Simplifying
5x2 + 11x = 8

Reorder the terms:
11x + 5x2 = 8

Solving
11x + 5x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 11x + 5x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 11x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-1.6 + 2.2x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 2.2x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 2.2x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 2.2x + x2 = 0 + 1.6
2.2x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
2.2x + x2 = 1.6

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = 1.6 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 1.6 + 1.21

Combine like terms: 1.6 + 1.21 = 2.81
1.21 + 2.2x + x2 = 2.81

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 2.81

Calculate the square root of the right side: 1.676305461

Break this problem into two subproblems by setting 
(x + 1.1) equal to 1.676305461 and -1.676305461.

Subproblem 1

x + 1.1 = 1.676305461 Simplifying x + 1.1 = 1.676305461 Reorder the terms: 1.1 + x = 1.676305461 Solving 1.1 + x = 1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.676305461 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.676305461 + -1.1 x = 1.676305461 + -1.1 Combine like terms: 1.676305461 + -1.1 = 0.576305461 x = 0.576305461 Simplifying x = 0.576305461

Subproblem 2

x + 1.1 = -1.676305461 Simplifying x + 1.1 = -1.676305461 Reorder the terms: 1.1 + x = -1.676305461 Solving 1.1 + x = -1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.676305461 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.676305461 + -1.1 x = -1.676305461 + -1.1 Combine like terms: -1.676305461 + -1.1 = -2.776305461 x = -2.776305461 Simplifying x = -2.776305461

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.576305461, -2.776305461}

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